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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/52687

Title: Semi-analytical approach for torsion problems of a circular bar containing multiple holes and/or cracks
Authors: Shyh-Rong Kuo
Jeng-Tzong Chen
Ying-Te Lee
Contributors: 國立臺灣海洋大學:河海工程學系
Keywords: Torsional rigidity
Stress intensity factor
Degenerate kernel
Warping function
Crack
Date: 2019-10
Issue Date: 2019-12-20T01:26:12Z
Publisher: Scisence Journals
Abstract: Abstract: A semi-analytical approach of the null-field integral equation in conjunction containing the degenerate kernels is used to deal with the torsion problems of a circular bar with circular or elliptic holes and/or line cracks. In order to fully capture the elliptic geometry, the use of the addition theorem in terms of the elliptic coordinates plays an important role to expand the fundamental solution into the degenerate form. The boundary densities are expressed by using the eigenfunction expansion for the elliptic boundary. It is worthy of noting that the model of elliptic hole in companion with the limiting process of approaching the length of the semi-minor axis to zero is adopted to simulate the line crack. Besides, we also make the length of the semi-major axis close to the length of the semi-minor axis to approximate the circular boundary. By collocating the observation point exactly on the real boundary and matching the boundary conditions, a linear algebraic system is easily constructed to determine the unknown eigenfucntion coefficients. This approach can be seen as a semi-analytical manner since error purely attributes to the truncation of eigenfunction expansions and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. Finally, several numerical examples of a circular bar with circular or elliptic holes and/or line cracks are employed to show the validity of the proposed approach. Not only the torsional rigidity but also the stress intensity factors are calculated to compare with the available results in the literature.
Relation: 219(1)
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/52687
Appears in Collections:[系統工程暨造船學系] 期刊論文

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